This function builds the covariance matrix for a set of spatial locations, given the covariance parameters. According to the input options other results related to the covariance matrix (such as decompositions, determinants, inverse. etc) can also be returned.
varcov.spatial(coords = NULL, dists.lowertri = NULL,
cov.model = "matern", kappa = 0.5, nugget = 0,
cov.pars = stop("no cov.pars argument"),
inv = FALSE, det = FALSE,
func.inv = c("cholesky", "eigen", "svd", "solve"),
scaled = FALSE, only.decomposition = FALSE,
sqrt.inv = FALSE, try.another.decomposition = TRUE,
only.inv.lower.diag = FALSE, ...)The result is always list. The components will vary according to the input options. The possible components are:
the covariance matrix.
a square root of the covariance matrix.
the lower triangle of the inverse of covariance matrix.
the diagonal of the inverse of covariance matrix.
the inverse of covariance matrix.
a square root of the inverse of covariance matrix.
the logarithmic of the square root of the determinant of the covariance matrix.
an \(n \times 2\) matrix with the coordinates
of the data locations. If not provided
the argument dists.lowertri should be provided instead.
a vector with the lower triangle of the matrix
of distances between pairs of data points. If not provided
the argument coords should be provided instead.
a string indicating the type of the correlation
function. More details in the
documentation for cov.spatial.
Defaults are equivalent to the exponential model.
values of the additional smoothness parameter, only required by
the following correlation
functions: "matern", "powered.exponential", "cauchy" and
"gneiting.matern".
the value of the nugget parameter \(\tau^2\).
a vector with 2 elements or an \(ns \times 2\) matrix with the covariance parameters. The first element (if a vector) or first column (if a matrix) corresponds to the variance parameter \(\sigma^2\). second element or column corresponds to the correlation function parameter \(\phi\). If a matrix is provided each row corresponds to the parameters of one spatial structure. Models with several structures are also called nested models in the geostatistical literature.
if TRUE the inverse of covariance
matrix is returned. Defaults to FALSE.
if TRUE the logarithmic of the square root of the
determinant of the covariance
matrix is returned. Defaults to FALSE.
algorithm used for the decomposition and inversion of the covariance
matrix. Options are "chol" for Cholesky decomposition,
"svd" for singular value decomposition and "eigen" for
eigenvalues/eigenvectors decomposition. Defaults to "chol".
logical indicating whether the covariance matrix should
be scaled. If TRUE the partial sill
parameter \(\sigma^2\) is set to 1. Defaults to FALSE.
logical. If TRUE only the square root
of the covariance matrix is
returned. Defaults to FALSE.
if TRUE the square root of the inverse of covariance
matrix is returned. Defaults to FALSE.
logical. If TRUE and the argument
func.inv is one of "cholesky", "svd" or
"solve", the matrix decomposition or inversion is tested and,
if it fails, the argument func.inv is re-set to "eigen".
logical. If TRUE only the lower triangle and
the diagonal of the inverse of the covariance matrix are
returned. Defaults to FALSE.
for naw, only for internal usage.
Paulo J. Ribeiro Jr. paulojus@leg.ufpr.br,
Peter J. Diggle p.diggle@lancaster.ac.uk.
The elements of the covariance matrix are computed by the function
cov.spatial. Typically this is an auxiliary function called by other
functions in the geoR package.
Further information on the package geoR can be found at:
http://www.leg.ufpr.br/geoR/.